What is the value of cos(45)tan(30) ?

The value of cos(45)tan(30) is (sqrt(6))/6

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Popular >

cos(45)tan(30)

Solution

cos (4 5^{\circ}) tan (3 0^{\circ})

Solution

\frac{6}{6}

Decimal Notation

0.40824 \dots

Solution steps

cos (4 5^{\circ}) tan (3 0^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= \frac{2}{2} \cdot \frac{3}{3}

Simplify

\frac{2}{2} \cdot \frac{3}{3} : \frac{6}{6}

\frac{2}{2} \cdot \frac{3}{3}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{2 3}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{2 3}{6}

Factor

6 : 2 \cdot 3

Factor

6 = 2 \cdot 3

= \frac{2 3}{2 \cdot 3}

Cancel

\frac{2 3}{2 \cdot 3} : \frac{1}{2 3}

\frac{2 3}{2 \cdot 3}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}} 3}{2 \cdot 3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{3}{3 \cdot 2 ^{- \frac{1}{2} + 1}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{3}{3 \cdot 2 ^{\frac{1}{2}}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{3}{3 2}

Apply radical rule:

3 = 3^{\frac{1}{2}}

= \frac{3 ^{\frac{1}{2}}}{3 2}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{1}{2 \cdot 3 ^{- \frac{1}{2} + 1}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{2 \cdot 3 ^{\frac{1}{2}}}

Apply radical rule:

3^{\frac{1}{2}} = 3

= \frac{1}{2 3}

= \frac{1}{2 3}

Simplify

23 : 6

23

Apply radical rule:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= \frac{1}{6}

Rationalize

\frac{1}{6} : \frac{6}{6}

\frac{1}{6}

Multiply by the conjugate

\frac{6}{6}

= \frac{1 \cdot 6}{6 6}

1 \cdot 6 = 6

66 = 6

66

Apply radical rule:

a a = a

66 = 6

= 6

= \frac{6}{6}

= \frac{6}{6}

= \frac{6}{6}

Popular Examples

5000*cos(30.51)

5000 \cdot cos (30.5 1^{\circ})

(-113100)/(320.96*cos(180))

\frac{- 113100}{320.96 \cdot cos ( 18 0 ^{\circ} )}

5/(tan(31))

\frac{5}{tan ( 3 1 ^{\circ} )}

4cos^2((-pi)/4)

4 cos^{2} (\frac{- π}{4})

cot(-(13pi)/4)

cot (- \frac{13 π}{4})

Frequently Asked Questions (FAQ)

What is the value of cos(45)tan(30) ?
The value of cos(45)tan(30) is (sqrt(6))/6